2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58479We extend our family rigidity and vanishing theorems in [{\bf LiuMaZ}] to the Spin^c case. In particular, we prove a K-theory version of the main results of [{\bf H}], [{\bf Liu1}, Theorem B] for a family of almost complex manifolds.31 pagesK-Theory and HomologyAlgebraic TopologyDifferential Geometry14D05, 57R91text